This paper investigates the value of introducing a little flexibility into the classical n × n student-optimal stable matching (SOSM) problem. We define flexibility as the ability to relax stability constraints, and we aim to characterize the value of flexibility-the reduction in total rank across all students when a single flexible match is permitted. We find that this minimal intervention-affecting just one match out of n-can nevertheless generate system-wide efficiency gains. We first establish tight upper and lower bounds: in the best case, a single flexible match yields an aggregate rank reduction of more than n(n-3), more than if every student moved from their second-to-worst to their second-to-best choice; in the worst case, flexibility yields no improvement. We then explore how preference structure affects the value of flexibility. With mild randomness in preferences, the value of flexibility already scales as Θ̃(n) in expectation, though only Θ(log n) students strictly benefit from flexibility. In fully random markets, we show that flexibility continues to generate Ω(n) improvement in rank in expectation, with Θ̃(n) students strictly better off. This suggests that allowing even a single flexible match can improve the average rank across all students by a constant. Our theoretical findings are supported by simulations using both random and empirical preference profiles; the latter are based on data from the dating platform OkCupid. Across these environments, we find that the gains from flexibility remain significant under various practical constraints, showing that even greater improvements are possible when the flexible pair is chosen optimally and when a small number of flexible matches (rather than just one) are permitted. Overall, our results demonstrate that a little flexibility goes a long way in stable matching.